Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 52 12 2019 09 28 Single and Multi-objective Optimal Control Design by Genetic Programming and Comparison with Riccati Equation Solutions Single and Multi-objective Optimal Control Design by Genetic Programming and Comparison with Riccati Equation Solutions 3369 3382 3601 10.22060/mej.2019.16014.6258 FA Adel Mohamamdi Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran Nader Nariman-zadeh Department of Mechanical Engineering, Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran Ali Jamali Faculty of Mechanical Enginnering, University of Guilan, Rasht, Iran Journal Article 2019 03 19  Gaining the function of control signal that transfer the system states from initial to desired final conditions is one of the main issues related to the optimal control of modern systems. Optimal control signal is usually obtained by numerical solution (such as dynamic programming algorithm) or analytical solution (like Hamilton-Jacobi-Bellman or Riccati equations approaches) of a single-objective performance index which is a weighted combination of control effort and the fitness of system’s states. However, choosing proper weight coefficients in these approaches needs a lot of trial and error in addition to experience. In this papers, such time consuming procedures are eliminated by using Genetic programming in single and multi-objective optimization process to find those closed-form mathematical solutions of optimal control problems. In this way, it would be readily possible to trade-off among the objective functions using the obtained pareto-front of those solutions based on the needs of the control system designer. It will be shown that in the case of same weighting factors, the solution of the Riccati equation would also be obtained using the approach of this paper  Gaining the function of control signal that transfer the system states from initial to desired final conditions is one of the main issues related to the optimal control of modern systems. Optimal control signal is usually obtained by numerical solution (such as dynamic programming algorithm) or analytical solution (like Hamilton-Jacobi-Bellman or Riccati equations approaches) of a single-objective performance index which is a weighted combination of control effort and the fitness of system’s states. However, choosing proper weight coefficients in these approaches needs a lot of trial and error in addition to experience. In this papers, such time consuming procedures are eliminated by using Genetic programming in single and multi-objective optimization process to find those closed-form mathematical solutions of optimal control problems. In this way, it would be readily possible to trade-off among the objective functions using the obtained pareto-front of those solutions based on the needs of the control system designer. It will be shown that in the case of same weighting factors, the solution of the Riccati equation would also be obtained using the approach of this paper https://mej.aut.ac.ir/article_3601_62e7f2e090fe150ef8deb4466fdc81b3.pdf